Disorder operators are a type of nonlocal observables for quantum many-body systems, measuring the fluctuations of symmetry charges inside a region. It has been shown that disorder operators can reveal global aspects of many-body states that are otherwise difficult to access through local measurements. We study the disorder operator for U(1) (charge or spin) symmetry in two-dimensional Fermi and non-Fermi liquid states, using the multidimensional bosonization formalism. For a region $A$, the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asymptotically as $l_{A}ln{l}_A$, with $l_A$ being the linear size of the region $A$. We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of the Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point the scaling behavior of the charge disorder operators is drastically modified to $l_A{ln}^2{l}_A$. We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as $l_A$.

Close

PrevNext

View figure in article

• Composite fermions
• Fermi surface
• Bosonization
• Fermi liquid theory
• Non-Fermi-liquid theory
• Random phase approximation